what is the inverse of : g(t)=-(8\27)t to the third power

g(t)  =  -(8/27)t³

Replace 'g(t)' with 't', and 't' with 'g^-1(t)':

--->   t  =  -(8/27)[g^-1(t)]³

Now, solve for g^-1(t):

  --  Divide both sides by -(8/27)         --->   -(27/8)t  =  [g^-1(t)]³

  --  Find the cube root of both sides    --->  -3/2·t^1/3  =  g^-1(t)

--->  g^-1(t)  =  -3/2·t^1/3